HARMONIC ANALYSIS AND PREDICTION OF TIDES all 
| a= 
Sh ne sis mae (298) 
a=0 
209. The upper part of Form 194 (fig. 16) is designed for the compu- 
tation of the coefficients C, and S, in accordance with formulas (295) 
and (296) to take account of the 24 constituent hourly means. 
It is now desired to express each constituent in the form 
y=A cos (p 6+ a) (299) 
or using a more specialized notation by 
y=A cos (p 6—¢) (300) 
By trigonometry 
A cos (p 6—¢)=A cos ¢ cos p 9+ A sin ¢ sin p 0 (301) 
=C, cos p 6+S8, sin p 6 
in which C5_ tA cost and=2:S)—AlsiniG (302) 
Therefore, 
_S» 
tan CSG (303) 
and 
= p= VOTE (304) 
cos MsiniG 
Substituting in formulas (303) and (304) the values of C, and S, from 
formulas (295) and (296), the corresponding values for A and ¢ may 
be obtained. Substituted in formula (300), these furnish an ap- 
proximate representation of one of the tidal constituents, but a further 
processing is necessary in order to obtain the mean amplitude and 
epoch of the constituent. 
AUGMENTING FACTORS 
210. In the usual summations with the primary stencils for all the 
short period constituents, except constituent S, the hourly ordinates 
which are summed in any single group are scattered more or less 
uniformly over a period from one-half of a constituent hour before 
to one-half of a constituent hour after the exact constituent hour 
which the group represents. Because of this the resulting mean will 
differ a little from the true mean ordinate that would be obtained if 
all the ordinates included were read on the exact constituent hour, as 
with constituent S, and the amplitude obtained will be less than the 
true amplitude of the constituent. The factor necessary to take 
account of this fact is called the augmenting factor. 
211. Let any constituent be represented by the curve 
y=A cos (at+a) (305) 
in which 
A=the true amplitude of the constituent 
a=the speed of the constituent (degrees per solar hours) 
t=variable time (expressed in solar hours) 
a=any constant. 
